A certain car is capable of accelerating at a
uniform rate of 0.81 m/s
What is the magnitude of the car’s displacement as it accelerates uniformly from a speed
of 82 km/h to one of 97 km/h?
Answer in units of m.
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Answers & Comments
Verified answer
Hi!
Since we know the the acceleration we know the rate at which velocity changes should be in equal time intervals
V= 97 km/h or 26.94 m/s
V0= 82 km/h or 22.78 m/s
a = 0.81 m/s^2
now using the formula
v^2 -v0^2 / 2a = d or x
(26.94)^2 - (22.78)^2 / 2(0.81) = x
x = 127.68 meters approximately
therefore distance travelled is 1.3*10^2 meters if it is in 2 sig figs.
Btw just incase you didn't understand how i got that formula
What i would do is first find the t
t = v-v0/a
and substitute that to find distance. We know that distance is (v1+v2)/2 * t
so instead of t i would substitute this
(v+v0)(v-v0/a)/2
which would be v^2-v0^2/2a = d or x
Hope that helps! Its just deriving the formula
And incase your not comfortable with the conventions for the variables i have used
v = velocity final
v0 = initial velocity
d or x = displacement
a = acceleration!
hope this helps! Good luck.
eighty one Km/h = eighty one * a million,000 / 3600 = 22.5 m/s ninety 4 Km/h = ninety 4 * a million,000 / 3600 = 26.11 m/s Vt^2 = V0^2 + 2 * a * S 26.11^2 = 22.5^2 + 2 * 0.86 * S 681.seventy 3 = 506.25 + a million,72 * S a hundred seventy five.40 8 = a million.72 * S S = 102 m
82 kph = 22.7777778 m/s
97 kph = 26.9444444 m/s
Time taken = (26.9444444 - 22.7777778) / 0.81
= 5.14s
Distance = 22.78*5.14 + 0.5*0.18*5.14^2 = 119.47